Unit size effect elimination method for finite element simulation of concrete structure damage

Abstract

The invention discloses an element size effect elimination method for concrete structure damage finite element simulation, which comprises the following steps of: 1, performing finite element mesh generation on a concrete structure, endowing all elements with a concrete damage zone model based on a power law type tensile damage equation and initial model parameters, and establishing a concrete structure damage finite element model; step 2, obtaining size information of each unit in the concrete structure damage finite element model in the step 1, and adaptively calculating model parameters of each unit related to the size of the unit based on the size information of the unit; and step 3, simulating a concrete structure loading process by using the model parameters calculated in the step 2 to obtain a concrete structure damage finite element simulation result in which the unit size effect is eliminated. The method breaks through the bottleneck that the unit size effect in concrete structure damage finite element simulation cannot be eliminated in the prior art, and has wide application prospects in the process of objectively simulating concrete structure damage evolution.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation of concrete structures, and in particular to a method for eliminating element size effects in finite element simulation of concrete structure damage. Background Technology

[0002] Numerous concrete structures are key components of infrastructure systems, prevalent in industries such as water conservancy and hydropower, civil engineering, and transportation. During their service life, concrete structures are subjected to various loads in complex environments, making them highly susceptible to damage of varying degrees, posing a serious threat to their long-term service life. Therefore, objectively simulating the damage evolution process of concrete structures under load is of great significance for reasonably evaluating their stress-deformation state and accurately assessing their safety.

[0003] Numerical methods, represented by the finite element method (FEM), are the primary means of simulating the damage evolution process of concrete structures. Specifically, this involves establishing a numerical simulation model of concrete structure damage based on a damage constitutive model and simulating the loading process to obtain the structural stress, deformation, and damage state at different loading stages. However, concrete is a typical quasi-brittle material with a complex microstructure. During tensile damage failure, it exhibits significant strain localization characteristics, resulting in simulation results in concrete structure damage finite element simulations being related to element size, i.e., an element size effect exists. This is mainly manifested in the energy dissipation caused by tensile damage cracking being related to element size; the smaller the element size, the steeper the load-displacement curve, making it impossible to guarantee the objectivity of the simulation results.

[0004] Currently, in finite element simulation of concrete structure damage, the element size effect is mainly addressed by adjusting the parameters of the local damage constitutive model based on the principle of objective energy dissipation. Specifically, the stress-strain relationship of the damage constitutive model is adjusted according to the element size. Different constitutive model parameters are used for elements with different sizes to satisfy the objectivity of energy dissipation during tensile damage and cracking of concrete. However, the existing technology has the following shortcomings:

[0005] (1) In the prior art, the parameters of the existing concrete damage constitutive model all have a reasonable range of values. Taking values ​​outside the reasonable range will cause the stress-strain relationship of concrete to be inconsistent with the mechanical properties of concrete. However, taking values ​​only within the reasonable range results in a small range of variation in the stress-strain relationship of concrete. In other words, when the stress-strain relationship of concrete corresponding to a certain unit size exceeds the above range, it will be impossible to reasonably adjust the parameters of the damage constitutive model based on the objective principle of energy dissipation.

[0006] (2) In the prior art, the adjustment of the parameters of the concrete damage constitutive model is carried out by the calculation simulation personnel based on experience. It is necessary to repeatedly adjust the parameters according to the energy dissipation results under different model parameters. The parameter adjustment takes a long time and involves a large amount of work.

[0007] (3) In the prior art, subjectivity is inevitable in adjusting the parameters of the concrete damage constitutive model, and it is impossible to guarantee that the model parameters of elements with different element sizes in the finite element simulation model have high adjustment accuracy. Summary of the Invention

[0008] Purpose of the invention: In order to overcome the shortcomings of the prior art, the present invention provides a method for eliminating the element size effect in finite element simulation of concrete structure damage. This method, by adopting a concrete damage zone model based on the power-law tensile damage equation and adaptively calculating model parameters related to element size, breaks through the bottleneck of existing technologies that cannot eliminate the dependence of concrete structure damage finite element simulation results on element size. It has broad application prospects in the objective simulation of concrete structure damage evolution.

[0009] Technical solution: To achieve the above technical objectives, the present invention adopts the following technical solution:

[0010] A method for eliminating element size effects in finite element simulation of concrete structure damage includes the following steps:

[0011] Step 1: Perform finite element mesh generation on the concrete structure, assign the concrete damage zone model based on the power-law tensile damage equation and the initial model parameters to all elements, and establish a finite element model of concrete structure damage.

[0012] Step 2: Obtain the element size information of each element in the finite element model of concrete structure damage described in Step 1, and adaptively calculate the model parameters related to the element size of each element based on the element size information.

[0013] Step 3: Using the model parameters calculated in Step 2, simulate the loading process of the concrete structure to obtain finite element simulation results of concrete structure damage that have eliminated the element size effect.

[0014] As a further preferred embodiment of the method described above, in step 1, the concrete damage zone model adopts a local form of stress-strain relationship, specifically expressed as follows:

[0015] (1)

[0016] In the formula, For stress tensor; Let the initial elasticity tensor be used; For local strain tensor; As a damage variable, , and These are the tensile damage variables and the compressive damage variables, respectively. and These are the tensile damage weighting coefficient and the compressive damage weighting coefficient, respectively; the compressive damage variable... The specific calculation expression is as follows:

[0017] (2)

[0018] In the formula, For peak tensile strain, , It is the uniaxial tensile strength. This is the initial elastic modulus;

[0019] and For the evolution control parameters of the pressure damage variable;

[0020] For equivalent change, , The main response is to adapt to change, and the positive aspect is to pull. Macauley brackets, .

[0021] As a further preferred embodiment of the method described above, in step 1, the specific expression of the power-law tensile damage equation is as follows:

[0022] (3)

[0023] In the formula, The ultimate tensile strain; and For the control parameters of tensile damage variable evolution; , , All are fracture energy and the width of the damage zone The function, i.e. , , The corresponding initial model parameters are the initial values ​​of the ultimate tensile strain. and the initial values ​​of the control parameters for the evolution of tensile damage variables. and .

[0024] As a further preferred embodiment of the method described above, in step 1, the initial model parameters include the initial elastic modulus. Poisson's ratio Uniaxial tensile strength Control parameters for the evolution of compressive damage variables and fracture energy Initial value of ultimate tensile strain and the initial values ​​of the control parameters for the evolution of tensile damage variables. and .

[0025] As a further preferred embodiment of the method described above, in step 2, the unit size information of the unit, for a two-dimensional unit, refers to the unit area. For a three-dimensional element, it refers to the element volume. .

[0026] As a further preferred embodiment of the method described above, in step 2, the model parameters related to the unit size include the damage band width. Ultimate tensile strain and tensile damage variable evolution control parameters and Among them, the width of the damage zone The ultimate tensile strain is determined based on the element size information. Based on and , , Corresponding fracture energy density and the initial values ​​of the ultimate tensile strain of the initial model parameters. and fracture energy Calculation determined the control parameters for the evolution of tensile damage variables. and Determined through optimized inversion calculations.

[0027] As a further preferred embodiment of the above method of the present invention, in step 2, the adaptive calculation of the model parameters related to the unit size of each unit means that the model parameters related to the unit size of each unit in the finite element simulation model of concrete structure damage are calculated and determined based on the unit size information and the initial model parameters of that unit.

[0028] As a further preferred embodiment of the method described above, step 2 includes the following sub-steps:

[0029] Step 2-1 Select an element A from the finite element simulation model of concrete structure damage;

[0030] Step 2-2 Calculate the width of the damage zone in unit A. The specific formula is as follows:

[0031] (4)

[0032] Step 2-3 Calculate the ultimate tensile strain of element A The specific formula is as follows:

[0033] (5)

[0034] In the formula, with , , Corresponding fracture energy density The specific calculation formula is as follows:

[0035] (6)

[0036] In the formula, It is a uniaxial tensile stress; For uniaxial tensile inelastic strain, , It is a uniaxial tensile strain;

[0037] Step 2-4 Calculate the initial value of the ultimate tensile strain Initial values ​​of control parameters for tensile damage variable evolution and Corresponding damage band width The specific formula is as follows:

[0038] (7)

[0039] Steps 2-5 Calculation and ratio The specific formula is as follows:

[0040] (8)

[0041] Steps 2-6: Plot the stress-inelastic strain curves corresponding to the initial model parameters. ~ The curve, in ~ Select N data points on the curve, extract the stress and inelastic strain data at each data point, and obtain the results. , , The corresponding N sets of stress and inelastic strain data ( , ), i = 1, 2, ..., N;

[0042] Steps 2-7: Based on the stress and inelastic strain data obtained in Step 2-6 ( , ) (i=1,2,…,N), use replace The ultimate tensile strain of element A is obtained. Tensile damage variable evolution control parameters and The corresponding N sets of stress and inelastic strain data ( , ), i = 1, 2, ..., N;

[0043] Step 2-8 Based on the results obtained in Step 2-6 ( , ), i=1,2,…,N and obtained from step 2-7 ( , (i=1,2,…,N), establish control parameters for optimizing the evolution of tensile damage variables during inversion. and objective function The specific expression is as follows:

[0044] (9)

[0045] In the formula, ; ;

[0046] Step 2-9: Based on the objective function established in Step 2-8 The control parameters for the evolution of tensile damage variables were determined through optimized inversion calculations. and ;

[0047] Step 2-10 Repeat steps 2-1 to 2-9 to calculate and determine the model parameters related to each element and its size.

[0048] As a further preferred embodiment of the method described above, in steps 2-9, the objective function established in steps 2-8 is... Determined through optimized inversion calculation and The specific process is as follows: based on the objective function established in steps 2-8 It employs intelligent optimization algorithms and iterative updates. and The objective function value is gradually reduced. When the objective function value decreases to the convergence threshold, the iteration stops, and the result is calculated using the objective function value corresponding to the value at which the iteration stopped. and As determined through optimized inversion calculation and .

[0049] As a further preferred embodiment of the above-mentioned method of the present invention, in step 3, the specific process of simulating the concrete structure loading process and obtaining the finite element simulation results of concrete structure damage that eliminates the element size effect is as follows: the concrete structure loading process is divided into M incremental steps. For any incremental step, the finite element equilibrium iteration is carried out to obtain the finite element simulation results of concrete structure damage under that incremental step. The number of incremental steps M is set according to the magnitude of the load to be applied and the simulation accuracy of the structural damage evolution process.

[0050] Beneficial Effects: This invention proposes a method for eliminating the element size effect in finite element simulation of concrete structure damage by employing a concrete damage zone model based on a power-law tensile damage equation and adaptively calculating model parameters related to element size. This method can ensure the objectivity of energy consumption due to concrete structure damage by adjusting model parameters related to element size, and avoid the problem of difficulty in reasonably adjusting model parameters when the element size varies greatly by using a power-law tensile damage equation. Furthermore, it can adaptively determine model parameters related to element size based on element size during the simulation process, breaking through the bottleneck of existing technologies that cannot eliminate the dependence of finite element simulation results of concrete structure damage on element size, and providing an effective solution for objectively simulating the evolution process of concrete structure damage. Attached Figure Description

[0051] Figure 1 This is a schematic diagram illustrating the implementation steps of the element size effect elimination method for finite element simulation of concrete structure damage according to the present invention.

[0052] Figure 2 This is a schematic diagram showing the geometry and dimensions of the concrete structure, boundary conditions, and load effects according to an embodiment of the present invention.

[0053] Figure 3 This is a schematic diagram of the finite element mesh generation results of a concrete structure according to an embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram of the damage evolution process of a concrete structure according to an embodiment of the present invention;

[0055] Figure 5 This is a schematic diagram of the load-displacement curve of a concrete structure according to an embodiment of the present invention. Detailed Implementation

[0056] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0057] like Figure 1 As shown, the method for eliminating element size effects in finite element simulation of concrete structure damage includes the following steps:

[0058] Step 1: Perform finite element mesh generation on the concrete structure, assign the concrete damage zone model based on the power-law tensile damage equation and the initial model parameters to all elements, and establish a finite element simulation model of concrete structure damage.

[0059] In this embodiment, as Figure 2 As shown, the concrete structure is a three-point bending simply supported beam with a length of 400mm and a cross-sectional dimension of 100mm×100mm. Vertical and horizontal displacement constraints are applied 50mm from the left end face of the beam, and normal vertical displacement constraints are applied 50mm from the right end face of the beam. A vertical displacement load u with a value of 0.14mm is applied at the middle of the top surface of the beam. Finite element meshing is performed on the concrete three-point bending simply supported beam. The element type is an eight-node hexahedral solid element, and the element geometry is a cube. To illustrate the beneficial effects of the present invention, the element side lengths are taken as 20mm, 10mm, and 5mm, respectively. The finite element meshing results (mesh I, II, III) corresponding to the above different element side lengths are as follows: Figure 3 As shown;

[0060] Assigning the concrete damage zone model based on the power-law tensile damage equation to all elements means that the concrete material constitutive model used in the finite element simulation model of concrete structure damage is the concrete damage zone model.

[0061] The concrete damage zone model uses a localized stress-strain relationship, as shown in the following expression:

[0062] (1)

[0063] In the formula, For stress tensor; Let the initial elasticity tensor be used; For local strain tensor; As a damage variable, , and These are the tensile damage variables and the compressive damage variables, respectively. and These are the tensile damage weighting coefficient and the compressive damage weighting coefficient, respectively. The specific calculation expression is as follows:

[0064] (2)

[0065] In the formula, For peak tensile strain, , It is the uniaxial tensile strength. This is the initial elastic modulus; and For the evolution control parameters of the pressure damage variable; For equivalent change, , The main response is to adapt to change, and the positive aspect is to pull. Macauley brackets, .

[0066] The specific expression for the power-law tensile damage equation is as follows:

[0067] (3)

[0068] In the formula, The ultimate tensile strain; and For the control parameters of tensile damage variable evolution; , , All are fracture energy and the width of the damage zone The function, i.e. , , The corresponding initial model parameters are the initial values ​​of the ultimate tensile strain. and the initial values ​​of the control parameters for the evolution of tensile damage variables. and .

[0069] Initial model parameters include the initial elastic modulus. Poisson's ratio Uniaxial tensile strength Control parameters for the evolution of compressive damage variables and fracture energy Initial value of ultimate tensile strain and the initial values ​​of the control parameters for the evolution of tensile damage variables. , .

[0070] In this embodiment, the initial model parameters used are shown in Table 1.

[0071] Table 1 Initial model parameters

[0072]

[0073] Step 2: Obtain the size information of each element and adaptively calculate the model parameters related to the element size for each element;

[0074] For two-dimensional cells, cell size information refers to the cell area. For a three-dimensional element, it refers to the element volume. .

[0075] In this embodiment, the volume of each cell in grids I, II, and III is 8000 mm². 3 1000mm 3 125mm 3 .

[0076] Model parameters related to element size include damage band width. Ultimate tensile strain and tensile damage variable evolution control parameters and Among them, the width of the damage zone The ultimate tensile strain is determined based on the element size information. Based on and , , Corresponding fracture energy density and the initial values ​​of the ultimate tensile strain of the initial model parameters. and fracture energy Calculation determined the control parameters for the evolution of tensile damage variables. and Determined through optimized inversion calculations.

[0077] Adaptive calculation of model parameters related to element size for each element means that the model parameters related to element size for each element in the finite element simulation model of concrete structure damage are calculated and determined based on the element size information and the initial model parameters.

[0078] Step 2 includes:

[0079] Step 2-1 Select an element A from the finite element simulation model of concrete structure damage;

[0080] Step 2-2 Calculate the width of the damage zone in unit A. The specific formula is as follows:

[0081] (4)

[0082] Step 2-3 Calculate the ultimate tensile strain of element A The specific formula is as follows:

[0083] (5)

[0084] In the formula, To and , , The corresponding fracture energy density is calculated using the following formula:

[0085] (6)

[0086] In the formula, It is a uniaxial tensile stress; For uniaxial tensile inelastic strain, , It represents uniaxial tensile strain.

[0087] Step 2-4 Calculate the initial value of the ultimate tensile strain Initial values ​​of control parameters for tensile damage variable evolution and Corresponding damage band width The specific formula is as follows:

[0088] (7)

[0089] Steps 2-5 Calculation and ratio The specific formula is as follows:

[0090] (8)

[0091] In this embodiment, the calculated values ​​of each cell in grids I, II, and III are... They are 1, 2, and 4 respectively.

[0092] Steps 2-6: Drawing and Initializing Model Parameters , , , , , The corresponding uniaxial tensile stress-inelastic strain curve ( ~ (curve), in ~ Select N data points on the curve, extract the stress and inelastic strain data at each data point, and obtain the results. , , The corresponding N sets of stress and inelastic strain data ( , ), i = 1, 2, ..., N;

[0093] In this embodiment, N is set to 15, and... , , The corresponding 15 sets of uniaxial tensile stress and inelastic strain data ( , ), i=1,2,…,15, as shown in Table 2.

[0094] Table 2 Uniaxial tensile stress and inelastic strain data under initial model parameters

[0095] Uniaxial tensile stress (MPa) Inelastic strain 3.00000 0.00000 2.37296 0.00074 1.88507 0.00142 1.50267 0.00205 1.19381 0.00263 0.94616 0.00320 0.74570 0.00373 0.57619 0.00425 0.43782 0.00475 0.32109 0.00525 0.22716 0.00573 0.15025 0.00621 0.09156 0.00667 0.03328 0.00734 0.01000 0.00800

[0096] Step 2-7 Based on the results obtained in Step 2-6 ( , ), i=1,2,…,N, use replace Get and , , The corresponding 15 sets of stress and inelastic strain data ( , ), i = 1, 2, ..., N;

[0097] In this embodiment, using replace The ultimate tensile strain of each element in the obtained meshes I, II, and III compared to element A Tensile damage variable evolution control parameters and The corresponding 15 sets of uniaxial tensile stress and inelastic strain data ( , ), i=1,2,…,15, as shown in Table 3.

[0098] Table 3 Uniaxial tensile stress and inelastic strain data for each element in meshes I, II, and III

[0099]

[0100] Step 2-8 Based on the results obtained in Step 2-6 ( , ), i=1,2,…,N, and obtained from step 2-7 ( , ), i=1,2,…,N, establish a system for optimizing the inversion and objective function The specific expression is as follows:

[0101] (9)

[0102] In the formula, ; .

[0103] Step 2-9: Based on the objective function established in Step 2-8 Based on intelligent optimization algorithms, iterative updates and This gradually reduces the objective function value, and the convergence threshold of the objective function is determined through optimization and inversion calculations. and .

[0104] In this embodiment, the intelligent optimization algorithm used is the asynchronous particle swarm optimization algorithm.

[0105] Based on the objective function established in steps 2-8 Determined through optimized inversion calculation and The specific process is as follows: based on the objective function established in steps 2-8 An intelligent optimization algorithm is used to iteratively update the control parameters for the evolution of tensile damage variables. and The objective function value is gradually reduced. When the objective function value decreases to the convergence threshold, the iteration stops, and the control parameters are evolved using the tensile damage variable corresponding to the objective function value at the time of stopping iteration. and As the evolution control parameter of the tensile damage variable determined through optimized inversion calculation. and .

[0106] In this embodiment, the convergence threshold of the objective function for optimization inversion is set to 0.01.

[0107] Step 2-10: Repeat steps 2-1 to 2-9 to calculate and determine the damage band width, a model parameter related to the element size, for each element. Ultimate tensile strain and tensile damage variable evolution control parameters and .

[0108] In this embodiment, the model parameters related to the element size of each element in the adaptively calculated meshes I, II, and III are shown in Table 4.

[0109] Table 4. Model parameters related to element size in adaptive calculation

[0110]

[0111] Step 3: Simulate the concrete structure loading process to obtain finite element simulation results of concrete structure damage after eliminating element size effects. The specific process for simulating the concrete structure loading process and obtaining finite element simulation results of concrete structure damage after eliminating element size effects is as follows: Divide the concrete structure loading process into M incremental steps. For any incremental step, perform finite element equilibrium iteration to obtain the finite element simulation results of concrete structure damage under that incremental step. The number of incremental steps, M, is set according to the magnitude of the required applied load and the simulation accuracy of the structural damage evolution process.

[0112] In this embodiment, the specific process of simulating the loading process of a concrete structure and obtaining the finite element simulation results of the concrete structure damage that eliminates the element size effect is as follows: the loading process of the concrete structure is divided into 10 incremental steps, that is, each incremental step applies a displacement increment load of 0.014mm. For any incremental step, the finite element equilibrium iteration is carried out to obtain the finite element simulation results of the concrete structure damage under that incremental step.

[0113] Figure 4 The following example illustrates the finite element simulation results of the damage evolution process of a concrete structure corresponding to grid I. Figure 5 The finite element simulation results of load (reaction force)-displacement curves for meshes I, II, and III are presented.

[0114] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the technical solutions of the present invention. Any technical solution that can be implemented based on the above embodiments without creative effort should be considered to fall within the scope of protection of the patent of the present invention.

Claims

1. A method for eliminating element size effects in finite element simulation of concrete structure damage, characterized in that, Includes the following steps: Step 1: Perform finite element mesh generation on the concrete structure, assign the concrete damage zone model based on the power-law tensile damage equation and the initial model parameters to all elements, and establish a finite element model of concrete structure damage. Step 2: Obtain the element size information of each element in the finite element model of concrete structure damage described in Step 1, and adaptively calculate the model parameters related to the element size of each element based on the element size information. Step 3: Using the model parameters calculated in Step 2, simulate the loading process of the concrete structure to obtain finite element simulation results of concrete structure damage that have eliminated the element size effect.

2. The method for eliminating element size effects in finite element simulation of concrete structure damage according to claim 1, characterized in that, In step 1, the concrete damage zone model adopts a local form of stress-strain relationship, the specific expression of which is as follows: （1） In the formula, For stress tensor; Let the initial elasticity tensor be used; For local strain tensor; As a damage variable, , and These are the tensile damage variables and the compressive damage variables, respectively. and These are the tensile damage weighting coefficient and the compressive damage weighting coefficient, respectively; the compressive damage variable... The specific calculation expression is as follows: （2） In the formula, For peak tensile strain, , It is the uniaxial tensile strength. This is the initial elastic modulus; and Control parameters for the evolution of compressive damage variables; For equivalent change, , The main response is to adapt to change, and the positive aspect is to pull. Macauley brackets, .

3. The method for eliminating element size effects in finite element simulation of concrete structure damage according to claim 1, characterized in that, In step 1, the specific expression of the power-law tensile damage equation is as follows: Below: (3) In the formula, For the ultimate tensile strain; and For the control parameters of tensile damage variable evolution; , , All are fracture energy and the width of the damage zone The function, i.e. , , The corresponding initial model parameters are the initial values ​​of the ultimate tensile strain. and the initial values ​​of the control parameters for the evolution of tensile damage variables. and .

4. The method for eliminating element size effect in finite element simulation of concrete structure damage according to claim 3, characterized in that, In step 1, the initial model parameters include the initial elastic modulus. Poisson's ratio Uniaxial tensile strength Control parameters for the evolution of compressive damage variables and fracture energy Initial value of ultimate tensile strain and the initial values ​​of the control parameters for the evolution of tensile damage variables. , .

5. The method for eliminating element size effects in finite element simulation of concrete structure damage according to claim 1, characterized in that, In step 2, the unit size information, for a two-dimensional unit, refers to the unit area. For three-dimensional elements, this refers to the element volume. .

6. The method for eliminating element size effects in finite element simulation of concrete structure damage according to claim 1, characterized in that, In step 2, the model parameters related to the unit size include the damage band width. Ultimate tensile strain and tensile damage variable evolution control parameters and Among them, the width of the damage zone The ultimate tensile strain is determined based on the element size information. Based on the initial value of the ultimate tensile strain Initial values ​​of control parameters for tensile damage variable evolution , Corresponding fracture energy density and the initial values ​​of the ultimate tensile strain of the initial model parameters. and fracture energy Calculation determined the control parameters for the evolution of tensile damage variables. and Determined through optimized inversion calculations.

7. The method for eliminating element size effects in finite element simulation of concrete structure damage according to claim 1, characterized in that, In step 2, the adaptive calculation of model parameters related to the element size of each element means that the model parameters related to the element size of each element in the finite element simulation model of concrete structure damage are calculated and determined based on the element size information and the initial model parameters.

8. The method for eliminating element size effect in finite element simulation of concrete structure damage according to claim 6, characterized in that, Step 2 includes the following sub-steps: Step 2-1: Select an element A from the finite element simulation model of concrete structure damage; Step 2-2: Calculate the damage band width of element A The specific formula is as follows: （4） Steps 2-3: Calculate the ultimate tensile strain of element A The specific formula is as follows: （5） In the formula, is related to the initial value of the ultimate tensile strain. Initial values ​​of control parameters for tensile damage variable evolution , Corresponding fracture energy density The specific calculation formula is as follows: （6） In the formula, It is a uniaxial tensile stress; For uniaxial tensile inelastic strain, , It is a uniaxial tensile strain; Steps 2-4: Calculate the initial values ​​of the ultimate tensile strain. Initial values ​​of control parameters for tensile damage variable evolution and Corresponding damage band width The specific formula is as follows: （7） Steps 2-5: Calculation and ratio The specific formula is as follows: （8） Steps 2-6: Plot the stress-inelastic strain curves corresponding to the initial model parameters. ~ The curve, in ~ N data points are selected on the curve, and the stress and inelastic strain data at each data point are extracted to obtain the initial value of the ultimate tensile strain. Initial values ​​of control parameters for tensile damage variable evolution , The corresponding N sets of stress and inelastic strain data ( , ), where i = 1, 2, ..., N; Step 2-7: Based on the stress and inelastic strain data obtained in Step 2-6 ( , ), i=1,2,…,N, use replace The ultimate tensile strain of element A is obtained. Tensile damage variable evolution control parameters and The corresponding N sets of stress and inelastic strain data ( , ), i = 1, 2, ..., N; Step 2-8 Based on the results obtained in Step 2-6 ( , ), where i=1,2,…,N and the result obtained in step 2-7 ( , (i=1,2,…,N), establish control parameters for optimizing the evolution of tensile damage variables during inversion. and objective function The specific expression is as follows: （9） In the formula, ; ; Step 2-9: Based on the objective function established in Step 2-8 The control parameters for the evolution of tensile damage variables were determined through optimized inversion calculations. and ; Step 2-10 Repeat steps 2-1 to 2-9 to calculate and determine the model parameters related to each element and its size.

9. The method for eliminating element size effect in finite element simulation of concrete structure damage according to claim 8, characterized in that, In steps 2-9, the objective function established in step 2-8 is used... Determined through optimized inversion calculation and The specific process is as follows: based on the objective function established in steps 2-8 It employs intelligent optimization algorithms and iterative updates. and The objective function value is gradually reduced. When the objective function value decreases to the convergence threshold, the iteration stops, and the result is calculated using the objective function value corresponding to the value at which the iteration stopped. and As determined through optimized inversion calculation and .

10. The method for eliminating element size effects in finite element simulation of concrete structure damage according to claim 1, characterized in that, In step 3, the specific process of simulating the concrete structure loading process and obtaining the finite element simulation results of concrete structure damage that eliminates the element size effect is as follows: the concrete structure loading process is divided into M incremental steps. For any incremental step, the finite element equilibrium iteration is carried out to obtain the finite element simulation results of concrete structure damage under that incremental step. The number of increment steps, M, is set according to the magnitude of the load to be applied and the simulation accuracy of the structural damage evolution process.

Images